Temporary work permits are almost impossible to get as an English teacher. Most foreigners stay and teach on a normal tourist visa. Rarely, except for at large, traditional schools, the employer requests that the foreigner has a work visa. In fact, there are certain fiscal benefits when they hire a person who is "illegal."
As a tourist, you are allowed to stay a max. of 180 days per year. After the 180 days are up, the foreigner must leave, or he'll be subject to a fine once he attempts to do so later (in theory, because immigration doesn't always study the passport carefully enough to notice anything... BUT IT HAPPENS). It is NOT an option to go for a "border run."

This issue is really a pain in the a.., but If you live in Rio de Janeiro, or are willing to come to the city, I may be able to give advice on how to avoid becoming illegal. Feel free to write an e-mail to viking_dk@hotmail.com.